# Evaluate the following integrals.int_0^{pi/2}4^{sin x}cos xdx

Evaluate the following integrals.
${\int }_{0}^{\frac{\pi }{2}}{4}^{\mathrm{sin}x}\mathrm{cos}xdx$

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$\text{Integration}$
${\int }_{0}^{\frac{\pi }{2}}{4}^{\mathrm{sin}x}\mathrm{cos}xdx$
$\text{Let us take a substitution}$
$\mathrm{sin}x=z$
$\mathrm{cos}xdx=dz$
${\int }_{0}^{1}{4}^{z}dz$
$=\left[\frac{{4}^{z}}{\mathrm{ln}4}{\right]}_{0}^{1}=\frac{4}{\mathrm{ln}4}-\frac{1}{\mathrm{ln}4}$
$=\frac{3}{\mathrm{ln}4}$
$\text{This is the required answer.}$